Suppressing the spiking of a synchronized array of Izhikevich neurons

Nonlinear Dynamics - The aim of this research work is to investigate the synchronization and desynchronization of an array of non-identical Izhikevich neurons in a star-like configuration. Both...     

Solving Painlevé paradox: (P–R) sliding robot case

For a rigid body or a multibody system sliding on a rough surface, a range of uncertainty or non-uniqueness of solution could be found, which is termed: Painlevé paradox. Painlevé paradox is the reason of a wide range of undesired bouncing motions which are observed during sliding. As Painlevé paradox is a practical problem in case of multibody systems, this research work has investigated that paradox. In this research work, the condition leading to Painlevé paradox has been determined for a general multibody system. Investigating the motion of a prismatic–revolute (P–R), sliding robot has been conducted. In order to solve the paradox and find the motion, a tangential impact is assumed at the contact point. The impact model has been developed and the paradox, consequently, has been solved. Consequently, the kinematics of the motion has been specified.     

Modified Parker-Sochacki method for solving nonlinear oscillators

A new approach is presented for solving nonlinear oscillatory systems. Parker-Sochacki method (PSM) is combined with Laplace-Padé resummation method to obtain approximate periodic solutions for three nonlinear oscillators. The first one is Duffing oscillator with quintic nonlinearity which has odd nonlinearity. The second one is Helmholtz oscillator which has even nonlinearity. The last one is a strongly nonlinear oscillator, namely; relativistic harmonic oscillator which has a fractional order nonlinearity. Solutions are also obtained using Runge-Kutta numerical method (RKM) and Lindstedt-Poincare method (LPM). However, the LPM could not be used to solve the relativistic harmonic oscillator since it is a strongly nonlinear oscillator. The comparison between these solutions shows that the convergence zone for the Parker-Sochacki with Laplace-Padé method (PSLPM) is remarkably increased compared to PSM method. It also shows that the PSLPM solutions are in excellent agreement with LPM solutions for Duffing oscillator and are superior to LPM solutions in case of Helmholtz oscillator. The PSLPM succeeded to give an accurate periodic solution for the relativistic harmonic oscillator. For a wide range of solution domain, comparing PSLPM with RKM prove the correctness of the PSLPM method. Hence, the PSLPM method can be used with satisfied confidence to solve a broad class of nonlinear oscillators.